Convexity, complexity, and high dimensions

  • Stanislaw J. Szarek

    Case Western Reserve University, Cleveland, United States
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We discuss metric, algorithmic and geometric issues related to broadly understood complexity of high dimensional convex sets. The specific topics we bring up include metric entropy and its duality, derandomization of constructions of normed spaces or of convex bodies, and different fundamental questions related to geometric diversity of such bodies, as measured by various isomorphic (as opposed to isometric) invariants.